Light Diffraction: Explaining Airy Equation

[a-lbi]

What describes Airy equation in theoretical description of light diffraction?

 

[Claude Bile]

The Airy disc is the diffraction pattern you get for a circular aperture.

http://en.wikipedia.org/wiki/Airy_disc

Claude.

 

[a-lbi]

Thank you for your response. I've read this article. But there are no answers for my question.

Writing more precisly. I would like to see derivation from (for instance) wave equation to get Airy equation in a light diffraction problem.

 

[Claude Bile]

To find a diffraction pattern for a given aperture, you need to apply the theory of Fraunhofer diffraction.

To do this, define an aperture function in cylindrical coordinates as follows;

a(r) = 1 for r less than or equal to a.
a(r) = 0 for r greater than a.

Where a is the radius of the aperture.

The resultant diffraction pattern is a 2D Fourier transform of this function (i.e. the Airy function). I'm sure you can find the gory details of this calculation somewhere (or maybe post in the math forums).

Claude.

 

[a-lbi]

Thank you for your response. I can see that the problem is to get Airy equation from the two dimensional Fourier integral equation. If I have some time I will try to follow the way.